The method of homogeneous solutions and biorthogonal expansions in the plane problem of the theory of elasticity for an orthotropic body
type: Item
instance of: scholarly article
title: The method of homogeneous solutions and biorthogonal expansions in the plane problem of the theory of elasticity for an orthotropic body
zbMATH Open document ID: 0887.73005
DOI: 10.1016/0021-8928(96)00014-7
author: V. V. Vasil'ofev
author: S. A. Lur'e
published in: Journal of Applied Mathematics and Mechanics
publication date: 1997-10-27T00:00:00Z
review text: The authors consider the plane problem in the theory of elasticity for a rectangular orthotropic strip with homogeneous boundary conditions on the longitudinal edges. An exact solution of the problem is constructed as an expansion in terms of characteristic elements of a generalized eigenvalue biharmonic problem. Biorthogonal functions for the system of characteristic elements are constructed explicitly, and double completeness of the characteristic elements is proved. The biorthogonality condition is shown to be equivalent to the generalized orthogonality relation of Papkovich type. For expansion of a special form, the biorthogonal system turns out to be identical with the system of characteristic elements. The authors obtain explicit expressions for the coefficients of the expansion, and for illustration apply the results to a semi-infinite strip whose end is subjected to self-balanced normal and shear forces.
Mathematics Subject Classification ID: 74B05
Mathematics Subject Classification ID: 74E10
zbMATH DE Number: 1042164
zbMATH Keywords: rectangular orthotropic strip
zbMATH Keywords: exact solution
zbMATH Keywords: generalized eigenvalue biharmonic problem
zbMATH Keywords: double completeness
zbMATH Keywords: generalized orthogonality relation of Papkovich type
zbMATH Keywords: semi-infinite strip
MaRDI profile type: Publication
full work available at URL: 0021-8928(96)00014-7
OpenAlex ID: W1993521032
cites work: On the completeness of a system of elementary solutions of the biharmonic equation in a semi-strip
cites work: Q3663581
cites work: Biorthogonal expansions in the first fundamental problem of elasticity theory
cites work: Q3265950
description: scientific article; zbMATH DE number 1042164